並列分散処理による2段階ランキングアルゴリズム

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(1)Vol.2014-DBS-160 No.20 Vol.2014-OS-131 No.20 Vol.2014-EMB-35 No.20 2014/11/18. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ฒྻ෼ࢄॲཧʹΑΔ 2 ஈ֊ϥϯΩϯάΞϧΰϦζϜ ෢Ҫɹྑଠ1,a). ৽ඒɹྱ඙1,b). ֓ཁɿ΢ΣϒάϥϑΛ࠶ߏங͢Δ͜ͱͰ, ϥϯΩϯάΞϧΰϦζϜΛ࣮ߦ͢ΔࡍʹඞཁͱͳΔղੳ࣌ؒΛ ୹ॖ͢Δ͜ͱ͕ՄೳͰ͋Δ. ϥϯΩϯάΞϧΰϦζϜͰղੳ͢Δࡍ, ฒྻ෼ࢄԽॲཧʹదԠͰ͖ΔΑ͏ʹ ͢Δ͜ͱͰ, ߋͳΔղੳ࣌ؒͷ୹ॖ͕‫ظ‬଴Ͱ͖Δ. ຊ‫ڀݚ‬͸, ΢ΣϒάϥϑΛ PageRank ͷղੳ͕ฒྻ෼ࢄ ॲཧՄೳͳάϥϑ΁࠶ߏஙΛߦ͍,PageRank ͷղੳΛߦ͏ࡍʹฒྻ෼ࢄॲཧΛ༻͍Δ͜ͱͰ, ղੳʹඞཁ ͳ࣌ؒΛ୹ॖ͢Δํ๏ΛఏҊ͢Δ. ຊఏҊํ๏͸, ΢ΣϒάϥϑͷϊʔυΛ SCAN ʹΑΓ Cluster ͱ Hub, Outlier ʹ෼ผ͠,Cluster ͱ Hub Ͱߏ੒͞ΕΔάϥϑͱ Cluster ಺ͷϊʔυͰߏ੒͞ΕΔάϥϑʹ΢Σϒ άϥϑΛ࠶ߏங͢Δ.Cluster ಺ͷάϥϑΛϥϯΩϯάΞϧΰϦζϜͰղੳ͢Δࡍ, ͓‫͍ޓ‬ͷ Cluster ͸ؔ܎ ੑ͕ແ͍ͨΊฒྻ෼ࢄॲཧ͕ՄೳʹͳΓ, ϥϯΩϯάΞϧΰϦζϜͷղੳ࣌ؒΛ୹ॖ͢Δ͜ͱ͕ग़དྷΔ.. 1. ͸͡Ίʹ. Cluster Λ࡞੒͢Δ.Cluster ʹଐ͞ͳ͔ͬͨϊʔυΛ 2 ͭ Ҏ্ͷ Cluster ͱͭͳ͕Γ͕͋ΔϊʔυΛ Hub ͱ͠,1 ͭͷ. ΢Σϒάϥϑͱ͸΢ΣϒΛάϥϑߏ଄Խͨ͠΋ͷͰ͋Γ,. Έͷ Cluster ͱͭͳ͕Γ͕͋ΔϊʔυΛ Outlier ͱ෼ผ͢. ϊʔυΛ΢Σϒϖʔδ, ΤοδΛϦϯΫͰද‫ͨ͠ݱ‬΋ͷͰ. Δ. ͜ΕʹΑΓ, ΢ΣϒάϥϑΛ Cluster ͱ Hub Ͱߏ੒͞Ε. ͋Δ. ΢ΣϒάϥϑΛղੳ͢Δ͜ͱͰ஌‫ݟ‬Λಋग़͢Δ͜ͱ. Δάϥϑͱ Cluster ಺ͷϊʔυͰߏ੒͞ΕΔάϥϑʹ΢Σ. ͕੝ΜʹߦΘΕ͓ͯΓ, ओͳղੳ๏ͱͯ͠ϥϯΩϯάΞϧ. ϒάϥϑΛ࠶ߏங͢Δ.Cluster ಺ͷάϥϑΛ PageRank Ͱ. ΰϦζϜͰ͋Δ PageRank[1] ΍ HITS[2], ίϛϡχςΟந. ղੳ͢Δࡍ, ͓‫͍ޓ‬ͷ Cluster ͸ؔ܎ੑ͕ແ͍ͨΊฒྻ෼. ग़ͱͯ͠ trawling[3] ΍ DBG[4] ͕͋Δ. ۙ೥Ͱ͸, ϊʔυ. ࢄॲཧ͕ՄೳʹͳΔ. ߋʹ, ΫϥελͰ੾Γ෼͚Δ͜ͱͰ 1. ਺ͱΤοδ਺͕਺ԯ‫ͳʹݸ‬Δάϥϑ͕ଘࡏ͍ͯ͠Δ. ྫ͑. ճ͋ͨΓͷ PageRank ͷղੳର৅ͱͳΔϊʔυͱΤοδ͕. ͹ Netcraft ͸ 2014 ೥ 10 ݄ͷ࣌఺Ͱ, શੈքͰগͳ͘ͱ΋. ‫ݮ‬গ͢Δ. Ҏ্ΑΓ,PageRank ͷղੳ࣌ؒΛ୹ॖ͢Δ͜ͱ. 10 ԯϖʔδҎ্ଘࡏ͢Δͱใࠂ͍ͯ͠Δ [5]. ΢Σϒάϥ. ͕ग़དྷΔ.. ϑ͸‫ۃ‬Ίͯେ‫ن‬໛ʹͳ͓ͬͯΓ, ղੳʹ͔͔Δ࣌ؒ͸๲େ ʹͳΔ. ྫ͑͹, ϥϯΩϯάΞϧΰϦζϜͰ͋Δ PageRank ͷ৔߹,N ‫ݸ‬ϊʔυ͕͋Δ࣌, ‫ྔࢉܭ‬͸ O(N 2 ) ͱͳΔ. ͦͷ. 2. ઌߦ‫ڀݚ‬ େ‫ن‬໛ͳ΢ΣϒάϥϑΛ࠶ߏங͢Δ͜ͱ͸, ΢Σϒάϥ. ͨΊ, େ‫ن‬໛ͳάϥϑʹରͯ͠ղੳ࣌ؒΛ୹ॖ͢Δํ๏͕. ϑΛ༻͍Δղੳํ๏ʹ͓͍ͯॏཁͳٕज़Ͱ͋Δ. ΢Σϒά. ඞཁͰ͋Δ. ղੳ࣌ؒΛ୹ॖ͢Δํ๏ [6],[7],[8],[9],[10] ͸ෳ. ϥϑͷ࠶ߏங͸େ͖͘෼͚Δͱ, ූ߸ԽʹΑΔํ๏ͱߏ଄. ਺͋Δ͕,1 ͭͱͯ͠΢ΣϒάϥϑΛ࠶ߏங͠ղੳ࣌ؒΛ. վྑʹΑΔํ๏ͷ 2 छྨʹ෼͔ΕΔ.. ୹ॖ͢Δํ๏͕‫͛ڍ‬ΒΕΔ. ຊ‫Ͱڀݚ‬͸, ϥϯΩϯάΞϧ ΰϦζϜͰ͋Δ PageRank ͷղੳ࣌ؒͷߋͳΔ୹ॖΛ໨ඪ. 2.1 ූ߸Խ. ͱ͠,PageRank ͷղੳΛฒྻ෼ࢄԽग़དྷΔΑ͏ͳ‫ܗ‬ঢ়ʹά. ූ߸ԽʹΑΔํ๏͸‫ط‬ଘͷσʔλѹॖΛ࢖༻͢Δ͔, ΢Σ. ϥϑΛ࠶ߏங, ղੳʹඞཁͳ࣌ؒΛ୹ॖ͢Δํ๏ΛఏҊ͢. ϒάϥϑͷಛ௃Λ༻͍Δํ๏Ͱ͋Δ.P. Boldi Β͸΢Σϒά. Δ. ຊํ๏Ͱ͸ Xu Β͕ఏҊͨ͠ SCAN[11] Λ༻͍ͯάϥϑ. ϥϑͷಛ௃ͱ WebGraph[12] ͱ͍͏໊ͷํ๏ΛఏҊͨ͠.. Λ࠶ߏங͢Δ.SCAN ͸ߏ଄తྨࣅ౓ʹ‫͍ͨͮج‬άϥϑΫ. ΢Σϒάϥϑͷಛ௃ͱͯ͠, ‫ॴہ‬ੑͱྨࣅੑ, ࿈ଓੑΛ‫͛ڍ‬. ϥελϦϯάํ๏ͷ 1 ͭͰ͋Δ. ߏ଄ྨࣅ౓ͷԼ‫ݶ‬஋Λࣔ. ͍ͯΔ.. ͢ᮢ஋ ε ͱ,Cluster ͷ࠷খϊʔυ਺Λࣔ͢ᮢ஋ЖΛ༻͍ͯ. ɾ‫ॴہ‬ੑ ɹଟ͘ͷ΢Σϒϖʔδ͸ಉ͡ϗετ಺ͷϖʔ. 1. a) b). ެཱ͸ͩͯ͜ະདྷେֶ Future University Hakodate [email protected] [email protected]. ⓒ 2014 Information Processing Society of Japan. δ ʹ ༠ ಋ ͢ Δ ͨ Ί ͷ Ϧ ϯ Ϋ Λ ‫ ؚ‬Μ Ͱ ͍ Δ. ྫ ͑ ͹,“home”,“next”,“previous”,“up” ͳͲͷϦϯΫ͕‫͛ڍ‬Β. 1.

(2) Vol.2014-DBS-160 No.20 Vol.2014-OS-131 No.20 Vol.2014-EMB-35 No.20 2014/11/18. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ΕΔ. ྫͰ্͛ͨϦϯΫ͸ಉ͡ϗετ಺ͰϦϯΫ͞ΕΔ͜ ͱ͕ଟ͍. ͭ·Γ, ϦϯΫ‫ͱݩ‬ϦϯΫઌͷ΢Σϒϖʔδͷ. URL Λൺֱ͢Δͱઌ಄จࣈྻ (ϗετ໊) ͕Ұக͠΍͘͢, ‫ॴہ‬ੑ͕‫ݱ‬ΕΔ. ɾྨࣅੑ ɹಉ͡ϗετͷ΢Σϒϖʔδ͸ࣅͨΑ͏ͳ΢Σϒϖʔδʹ ϦϯΫΛ࣋ͭ܏޲͕͋Δ. ྫ͑͹, ‫ڞ‬௨ͷςϯϓϨʔτͰ࡞ ੒͞ΕΔϖʔδͳͲ͕‫͛ڍ‬ΒΕΔ. ྫͰ্͛ͨϖʔδ͸ಉ. ਤ 1. ѹॖલ. ਤ 2. ѹॖ‫ޙ‬. ͡ߏ଄ͷϖʔδ͕ͨ͘͞Μ͋ΔͨΊಉ͡΢ΣϒϖʔδʹϦ. ͍Δ. ߏ଄վྑʹΑΔํ๏͸, ϊʔυ਺ͱΤοδ਺Λ࡟‫͢ݮ‬. ϯΫΛషΔ͜ͱ͕ଟ͍. ͭ·Γ, ಉҰϗετ໊ͷ΢Σϒϖʔ. Δ͜ͱ͕ग़དྷ͔ͭ,PageRank ͷղੳ࣌ؒΛ୹ॖ͢Δ͜ͱ͕. δͷϦϯΫͷ URL Λൺֱ͢Δͱ URL ͕Ұக͠΍͘͢, ྨ. ՄೳͰ͋Δ. Αͬͯຊ‫Ͱڀݚ‬͸,PageRank ͷղੳ࣌ؒͷ୹. ࣅੑ͕‫ݱ‬ΕΔ.. ॖΛ໨ඪͱ͍ͯ͠ΔͨΊߏ଄վྑʹΑΔํ๏Λ༻͍Δ. ै. ɾ࿈ଓੑ. དྷํ๏͸Τοδ਺΍ϊʔυ਺Λ࡟‫͠ݮ‬,PageRank ͷղੳ࣌. ɹ΢Σϒϖʔδʹ‫·ؚ‬ΕΔϦϯΫͷ URL ͸Ұఆͷ‫·ݻ‬Γ. ؒΛ୹ॖ͢Δ͜ͱʹ͸੒ޭ͍ͯ͠Δ. ຊ‫Ͱڀݚ‬͸, ΢Σϒά. Ͱ‫ݱ‬ΕΔ܏޲͕͋Δ. ྫ͑͹, େྔͷࣸਅΛ‫͍ͯ͠ࡌܝ‬Δ. ϥϑΛ PageRank ͷղੳ͕ฒྻ෼ࢄॲཧՄೳͳάϥϑ΁࠶. ϖʔδ͕‫͛ڍ‬ΒΕΔ. ྫͰ্͛ͨϖʔδ͸͋ΔҰఆͷ࿈ଓ. ߏஙΛߦ͍,PageRank ͷղੳΛߦ͏ࡍʹฒྻ෼ࢄॲཧΛ༻. ͨ͠ϦϯΫͷ‫·ݻ‬Γ͕ଘࡏ͢Δ. ͭ·Γ,URL Λࣙॻॱʹ੔. ͍Δ͜ͱͰ, ղੳʹඞཁͳ࣌ؒΛ୹ॖ͢Δํ๏ΛఏҊ͢Δ.. ྻ͠ॱʹ ID ΛׂΓ౰ͯΔͱ਺ࣈ͕࿈ଓ͠, ࿈ଓੑ͕‫ݱ‬ΕΔ.. P. Boldi Β͸্‫ه‬ͷಛ௃Λ༻͍ͯ, ࿈ଓੑΛར༻ͨࠩ͠. 3. SCAN. ෼ූ߸Խͱ, ‫ॴہ‬ੑͱྨࣅੑΛར༻ͨ͠ϥϯϨϯάεѹॖ. ఏҊํ๏Ͱ༻͍ΔΫϥελϦϯάํ๏ͷ SCAN[11] ʹ. Λ༻͍ͨํ๏ΛఏҊ͍ͯ͠Δ. ͜ΕʹΑΓ,1 ϦϯΫ͋ͨΓ. ͍ͭͯઆ໌͢Δ.SCAN ͸ΫϥελϦϯάର৅ͱ͢Δάϥ. 3.08bit ʹ཈͑Δ͜ͱʹ੒ޭ͍ͯ͠Δ.S. Tei Β͸ WebGraph. ϑ G = (V, E) Λղੳ͠, ߏ଄ྨࣅ౓ͷԼ‫ݶ‬஋Λࣔ͢ᮢ஋ ε. ͷࠩ෼ූ߸Խͷ‫ࢉޙ‬ज़ූ߸Λ༻͍Δ͜ͱͰ, ΢Σϒάϥϑ. ͱ,Cluster ͷ࠷খϊʔυ਺Λࣔ͢ᮢ஋ЖʹԠͨ͡ structure-. ͷ৘ใྔΛ WebGraph ΑΓ΋ 2 ׂ΄Ͳଟ͘࡟‫͢ݮ‬Δ͜ͱ. connected cluster Λ࡞੒͢Δ.Cluster ʹଐ͞ͳ͔ͬͨϊʔ. ʹ੒ޭ͍ͯ͠Δ [13]. ͔͠͠, ූ߸ԽʹΑΔํ๏Ͱ͸৘ใྔ. υ͸ Hub ͔ Outlier ͷ෼ผ͕ߦΘΕΔ.. Λ࡟‫͢ݮ‬Δ͜ͱ͸ग़དྷΔ͕, ϊʔυ਺ͱΤοδ਺Λ࡟‫ݮ‬ग़. ࠷ॳʹ͢΂ͯͷϊʔυʹରͯ͠ unclassfied ͷϥϕϧΛ. དྷͳ͍. ·ͨ, ෮߸Խ͢Δඞཁ͕͋Γ PageRank ͷղੳ࣌ؒ. ༩͑Δ.SCAN ͸ unclassfied ͷϥϕϧ͕෇͍͍ͯΔϊʔυ. ͕૿Ճͯ͠͠·͏. Αͬͯຊ‫Ͱڀݚ‬͸, ූ߸ԽʹΑΔํ๏͸. ʹରͯ͠, ͦͷϊʔυ͕ core Ͱ͋Δ͔Ͳ͏͔ͷ൑ఆΛߦ. ༻͍ͳ͍.. ͏.core ϊʔυ͸ Cluster ͷத৺ͱͳΔϊʔυͰ͋Δ.core Ͱ͋Δ͔൑அ͢ΔͨΊʹ͸, ର৅ͱͳΔ unclassfied ͳϊʔ. 2.2 ߏ଄վྑ. υͷߏ଄తྡ઀ϊʔυू߹ΛఆΊ, ߏ଄తྨࣅ౓Λ‫ࢉܭ‬, ᮢ. ߏ଄վྑ͸΢Σϒάϥϑͷߏ଄ΛҰ෦૊Έସ͑Δ͜ͱ. ஋ ε Λ༻͍ͯ ε-neighborhood Λࢉग़͢Δ͜ͱͰ core ͔Ͳ. Ͱϊʔυ਺΍Τοδ਺Λ࡟‫͢ݮ‬Δํ๏Ͱ͋Δ.G. Buehrer. ͏͔൑அ͢Δ͜ͱ͕ग़དྷΔ. ҎԼʹߏ଄తྡ઀ϊʔυू߹. Β͸ Virtual Node Miner[6] ͱ‫ݺ‬͹ΕΔ, Սۭͷϊʔυ (Ҏ. ͱߏ଄తྨࣅ౓,ε-neighborhood ͷఆٛΛ‫ه‬ड़͢Δ.. Լ,VN) Λ΢Σϒάϥϑʹૠೖ͢Δ͜ͱͰΤοδ਺Λ࡟‫ݮ‬. ɾߏ଄తྡ઀ϊʔυू߹. ͢Δํ๏ΛఏҊͨ͠.VN ͸ਤ 1 ͷΑ͏ͳ‫׬‬શ 2 ෦άϥϑ. v ∈ V Ͱ͋Δͱ͖, ߏ଄తྡ઀ϊʔυू߹͸ϊʔυ v ʹ. ͷதؒʹਤ 2 ͷΑ͏ʹૠೖ͢Δ. ͜ΕʹΑͬͯ, ϦϯΫΛ. ΤοδͰ઀ଓ͢Δϊʔυͱ, ϊʔυ v ࣗΒͰߏ੒͞ΕΔू. ू໿͠ϊʔυΛ࡟‫͍ͯ͠ݮ‬Δ.Virtual Node Miner ͸‫׬‬શ. ߹ Γ(v) Ͱද͞ΕΔ.. 2 ෦άϥϑͷ୳ࠪʹ࠷খ஋ಠཱஔ‫׵‬଒Λར༻͍ͯ͠Δ. ͜ ΕʹΑΓ, ϊʔυ਺໿ 7800 ສ, Τοδ਺໿ 3 ԯͷ΢Σϒά. Γ(v) = {v ∈ V | {v, w} ∈ E} ∪ {v}. ϥϑʹରͯ͠, ໿ 1700 ສͷ VN Λૠೖ͠Τοδ਺Λ 1/7. ɾߏ଄తྨࣅ౓. ʹ࡟‫ݮ‬ग़དྷͨͱ͍ͯ͠Δ. ย੉Β͸ LittleWeb[7] ͱ‫ݺ‬͹Ε. |Γ(v)| ͕ྡ઀ϊʔυू߹ʹ‫·ؚ‬ΕΔϊʔυ਺ͱ͢Δͱ, ϊʔ. Δ, ྨࣅϊʔυू໿ʹΑΔ΢Σϒάϥϑѹॖख๏ΛఏҊ͠. υ v, w ؒͷߏ଄తྨࣅ౓͸ σ(v, w) Ͱද͞ΕΔ.. ͨ.LittleWeb ͸ू໿ର৅ͱͳΔϊʔυΛ୳ࠪ͢ΔͨΊͷΫ ϥελϦϯάॲཧͱ, ΫϥελϦϯά݁ՌΛ༻͍ͨߏ଄վ. |Γ(v) ∩ Γ(w)| σ(v, w) = p |Γ(v)||Γ(w)|. ྑͷ 2 εςοϓͰ΢ΣϒάϥϑΛ࠶ߏங͍ͯ͠Δ. ͜Εʹ. ɾε-neighborhood. ΑΓ, ϊʔυΛ 67.3 ˋ, ΤοδΛ 56.3 ˋ࡟‫͍ͯ͠ݮ‬Δ. ߋ. ߏ ଄ ྨ ࣅ ౓ ͷ Լ ‫ ݶ‬஋ Λ ࣔ ͢ ᮢ ஋ ε Λ ༻ ͍ Δ ͜ ͱ Ͱ,ε-. ʹ,PageRank ͷղੳ࣌ؒΛ 67 ˋ୹ॖ͢Δ͜ͱʹ੒ޭͯ͠. neighborhood ͱද͞ΕΔ.. ⓒ 2014 Information Processing Society of Japan. 2.

(3) Vol.2014-DBS-160 No.20 Vol.2014-OS-131 No.20 Vol.2014-EMB-35 No.20 2014/11/18. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. Nε (v) = {w ∈ Γ(v)|σ(v, w) ≧ ε} ɾCore. ε ∈ R,µ ∈ N,v ∈ V ,|Nε (v)| Λϊʔυ v ͷ ε-neighborhood ͷϊʔυ਺ͱ͢Δͱ,core ͸ COREε,µ (v) Ͱද͞ΕΔ.. COREε,µ (v) ⇔ |Nε (v)| ≧ µ SCAN ͷ൑ఆʹΑΓϊʔυ͕ core Ͱ͋ͬͨ࣌, ͜ͷ core ϊʔυʹϢχʔΫ ID Ͱ͋Δ clusterID ͷϥϕϧΛ༩͑,core ϊʔυΛத৺ʹ structure-connected cluster Λ࡞੒͢Δ. ϊʔυ͕ core Ͱͳ͔ͬͨ࣌, ͦͷϊʔυʹ non-menber ͷ ϥϕϧΛ༩͑Δ. ɹ SCAN ͸ core ϊʔυͱ൑ఆ͞Εͨϊʔυ͔Β,structure. reachability Ͱ౸ୡՄೳͳϊʔυ͕ॴଐ͢Δ Cluster ʹ clusterID ͷϥϕϧΛ༩͑Δ. ࠷ॳʹ, Ωϡʔ Q ΁ core ϊʔυͷ ε-neighborhood ʹ‫·ؚ‬ΕΔ͢΂ͯͷϊʔυΛૠೖ͢Δ. ࣍ ʹ, Ωϡʔ Q ΁ૠೖ͞Εͨϊʔυʹରͯ͠,direct structure. reachability ͱͳΔϊʔυͷू߹Ͱ͋Δ R Λ‫ٻ‬ΊΔ. ҎԼʹ direct structure reachability ͱ structure reachability ͷఆ ٛΛ‫ه‬ड़͢Δ. ɾDirect structure reachability ϊʔυ v ͱϊʔυ w ʹ͓͚Δ direct structure reachability ͸ DirREACHε,µ (v, w) Ͱද͞ΕΔ.. 4. ఏҊํ๏ ຊ‫Ͱڀݚ‬͸, ΢ΣϒάϥϑΛ PageRank ͷղੳ͕ฒྻ෼ ࢄॲཧՄೳͳάϥϑ΁࠶ߏஙΛߦ͍,PageRank ͷղੳΛߦ ͏ࡍʹฒྻ෼ࢄॲཧΛ༻͍Δ͜ͱͰ, ղੳʹඞཁͳ࣌ؒΛ ୹ॖ͢Δํ๏ΛఏҊ͢Δ. ఏҊํ๏ʹΑΔ΢Σϒάϥϑղ ੳํ๏͸,3 ͭͷεςοϓͰߦΘΕΔ.. Step 1 SCAN Λ༻͍ͯ Web graph ΛΫϥελϦϯά͠ Cluster ͱ Hub,Outlier ʹϊʔυ෼ผ͢Δ. Step 2 PageRank ͷղੳ͕ฒྻ෼ࢄॲཧՄೳʹ͢ΔͨΊ,Cluster ͱ Hub Λ༻͍ͨ Compression graph ͱ Cluster ಺ ͷ΢ΣϒάϥϑͰ͋Δ Cluster graph ͷ 2 छྨͷάϥ ϑΛ࡞੒͠,Web graph Λ࠶ߏங͢Δ.. Step 3 Compression graph ͷ PageRank ஋Λࢉग़͠,Cluster ͱ Hub ʹΑΔϥϯΩϯάΛ࡞੒͢Δ. ͦͷ‫ޙ‬,Cluster. graph ͷ PageRank ஋Λࢉग़͠,Cluster ಺ͷϊʔυʹ ΑΔϥϯΩϯάΛ࡞੒͠, ͦΕͧΕͷϥϯΩϯάΛϚʔ δ͢Δ. ਤ 3 ͸ఏҊํ๏ͷྲྀΕΛਤࣔͨ͠΋ͷͰ͋Δ. Ҏ߱, ͦΕͧ ΕͷεςοϓΛৄ͘͠આ໌͢Δ.. DirREACHε,µ (v, w) ⇔ COREε,µ (v) ∧ Nε (v) ɾStructure reachability. ε ∈ R,µ ∈ N,v ∈ V ͱ͢Δͱ, ϊʔυ v ͱϊʔυ w ʹ͓͚ Δ Structure reachability ͸ REACHε,µ (v, w) Ͱද͞ΕΔ.. REACHε,µ (v, w) ⇔ ∃1 , ...vn ∈ V : v1 = v ∧ vn = w ∧ ∀i ∈ {1, ..., n − 1} : DirREACHε,µ (vi , vi+1 ) ϊʔυू߹ R Λ‫ٻ‬ΊΔʹ͸, Ωϡʔ Q ʹ‫·ؚ‬ΕΔશͯͷ ϊʔυͷߏ଄తྡ઀ϊʔυू߹ʹରͯ͠, ߏ଄తྨࣅ౓Λ‫ܭ‬ ࢉ͢Δ. ࠷‫ʹޙ‬ϊʔυू߹ R ʹ‫·ؚ‬ΕΔϊʔυͷॴଐ͢Δ. Cluster ͕ unclassfied ͷ࣌, ϊʔυΛΩϡʔ Q ΁ૠೖ͢Δ. ϊʔυू߹ R ʹ‫·ؚ‬ΕΔϊʔυ͕ unclassfied, ·ͨ͸ non-. menber ͷ࣌, ࡞੒ͨ͠ clusterID ͷϥϕϧΛ༩͑Δ. Ұ࿈ͷ ॲཧΛΩϡʔ Q ͕ͳ͘ͳΔ·Ͱߦ͍,structure-connected. cluster Λ࡞੒͠ଓ͚Δ. ɹ structure-connected cluster ͷ࡞੒͕ऴྃͨ͠Β,non-. menber ͷϥϕϧ͕෇͍ͨϊʔυʹରͯ͠ Hub ͱ Outlier ͷ෼ผΛߦ͏.non-menber ͷϥϕϧ͕෇͍ͨϊʔυ͕ 2 ͭ Ҏ্ͷҟͳΔ Cluster ͱ઀ଓ͍ͯ͠Δ৔߹, ͦͷϊʔυʹର. ਤ 3 ఏҊํ๏ͷྲྀΕ. ͯ͠ Hub ͷϥϕϧΛ༩͑Δ.1 ͭͷΈͷ Cluster ͱ઀ଓͯ͠ ͍Δ৔߹, ͦͷϊʔυʹରͯ͠ Outlier ͷϥϕϧΛ༩͑Δ. ɹҎ্ΑΓ, શͯͷϊʔυʹରͯ͠ϥϕϧ͕෇͚ऴΘΓ. SCAN ʹΑΔΫϥελϦϯά͸‫ྃ͢׬‬Δ. ⓒ 2014 Information Processing Society of Japan. 4.1 ΫϥελϦϯά ఏ Ҋ ํ ๏ Ͱ ͸,SCAN Λ ༻ ͍ ͯ Ϋ ϥ ε λ Ϧ ϯ ά Λ ߦ. 3.

(4) Vol.2014-DBS-160 No.20 Vol.2014-OS-131 No.20 Vol.2014-EMB-35 No.20 2014/11/18. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ͏.SCAN ͸άϥϑ಺ͷ͢΂ͯͷΤοδΛղੳ͠, ߏ଄త ྨࣅ౓ͷԼ‫ݶ‬஋Λද͢ᮢ஋ ε ͱ Cluster ͷ࠷খϊʔυ਺Λ ද͢ᮢ஋ЖʹԠͨ͡ Cluster Λ࡞੒͢Δ.Cluster ʹଐ͞ͳ ͔ͬͨϊʔυʹରͯ͠ 2 ͭҎ্ͷ Cluster ͱΤοδͰ઀ଓ ͞Ε͍ͯΔϊʔυ͸ Hub ͱ͠,1 ͭͷΈͷ Cluster ͱΤοδ Ͱ઀ଓ͞Ε͍ͯΔϊʔυ͸ Outlier ͱ෼ผ͢Δ. Ϋϥελ ϦϯάॲཧͷྫͰ͋Δਤ 4 ͸্ஈͷ Web graph ʹରͯ͠. SCAN Λ࣮ߦ͠, Լஈ͸ϊʔυΛ Cluster ͱ Hub,Outlier ʹ ෼ผͨ͠άϥϑͰ͋Δ.. ਤ 5. ࠶ߏஙͷྲྀΕ. ͏. ࣍ʹ Cluster ಺ͷ΢ΣϒάϥϑͰ͋Δ Cluster graph ͷ. PageRank ஋Λࢉग़͠,Cluster ಺ͷϊʔυʹର͢ΔϥϯΩϯ άΛ‫ٻ‬ΊΔ. ͜ͷ࣌,Cluster ֎ͷϊʔυؒͷΤοδ͸ແࢹ͢ Δ.Cluster graph ͷϥϯΩϯά͕‫·ٻ‬Γ࣍ୈ,Compression. graph ͷରԠ͢Δ Cluster ෦෼ʹ Cluster graph ͷϥϯΩϯ άΛૠೖ͠, ΢ΣϒάϥϑͷϥϯΩϯάΛ࡞੒͢Δ. ղੳͷ ਤ 4. ΫϥελϦϯάͷྲྀΕ. εςοϓͷྫͰ͋Δਤ 6 ͸, ॳΊʹ Compression graph Λ. PageRank Λ༻͍ͯϥϯΩϯάΛ࡞੒. ࣍ʹ,Cluster graph Λ PageRank Λ༻͍ͯϥϯΩϯάΛ࡞੒. ͜ͷ࣌,Hub ʹؔ. 4.2 ࠶ߏங SCAN ͷ݁ՌΛ༻͍ͯ Web graph Λ࠶ߏங͢Δ.Clus-. ͯ͠͸ಛʹૢ࡞͸ߦΘͳ͍. ࠷‫ʹޙ‬, ͦΕͧΕͷղੳ݁ՌͰ ͋ΔϥϯΩϯάΛϚʔδ͍ͯ͠Δ.. ter ͱ Hub Ͱߏ੒͞Εͨ΢ΣϒάϥϑͰ͋Δ Compression graph ͱ Cluster ಺ͷ΢ΣϒάϥϑͰ͋Δ Cluster graph ͷ. 4.4 ಛ௃. 2 छྨΛ࡞੒͢Δ. ࠶ߏஙͷྫͰ͋Δਤ 5 ͸ 4.1 Ͱ SCAN Λ. ຊ‫Ͱڀݚ‬͸, ΢ΣϒάϥϑΛ PageRank ͷղੳ͕ฒྻ෼. ༻͍ͯϊʔυΛ෼ผ্ͨ͠ஈͷάϥϑΑΓ,Cluster ͱ Hub. ࢄॲཧՄೳͳάϥϑ΁࠶ߏஙΛߦ͍,PageRank ͷղੳΛߦ. ͷΈͰߏ੒͞ΕΔ Compression graph ͱ,Cluster ಺ͷϊʔ. ͏ࡍʹฒྻ෼ࢄॲཧΛ༻͍Δ͜ͱͰ, ղੳʹඞཁͳ࣌ؒΛ୹. υͰߏ੒͞ΕΔ Cluster graph ʹ࠶ߏஙͨ͠΋ͷΛԼஈʹ. ॖ͢Δํ๏ΛఏҊ͍ͯ͠Δ͕, ฒྻ෼ࢄॲཧ͸ Cluster ಺ͷ. ࣔ͢.. ϊʔυʹର͢ΔϥϯΩϯάΛ‫ٻ‬ΊΔ࣌ʹߦΘΕΔ.Cluster ಺ͷϊʔυʹର͢ΔϥϯΩϯάΛ‫ٻ‬ΊΔࡍ,Cluster ֎ͷ. 4.3 PageRank. ϊʔυؒͷΤοδ͸ແࢹ͢ΔͨΊ, ͓‫͍ޓ‬ͷ Cluster ͸ؔ܎. PageRank Ͱͷղੳεςοϓ͸ 2 ͭͷεςοϓʹ෼͔Εͯ. ੑ͕ແ͘ͳΓ, ฒྻ෼ࢄॲཧ͕ՄೳͱͳΔ. ߋʹ,Cluster ͝. ͍Δ.1 ͭ໨͸ Compression graph ͷղੳ,2 ͭ໨͸ Cluster. ͱʹ PageRank ஋Λࢉग़͢ΔͨΊ,1 ճ͋ͨΓͷ PageRank. graph ͷղੳͰ͋Δ.2 ͭ໨ͷ Cluster graph ͷղੳ͸ฒྻ. ஋ͷࢉग़࣌ʹ‫ࢉܭ‬ର৅ͱͳΔϊʔυͱΤοδ͕‫ݮ‬গ͢Δ.. ෼ࢄॲཧΛ༻͍Δ. ਤ 6 ͸ղੳͷεςοϓΛਤࣔͨ͠΋ͷͰ. Ҏ্ΑΓ, ΢ΣϒάϥϑΛ PageRank Ͱղੳ͢Δࡍͷղੳ. ͋Δ. ࠷ॳʹ Cluster ͱ Hub Ͱߏ੒͞Εͨ΢ΣϒάϥϑͰ. ࣌ؒΛ୹ॖ͢Δ͜ͱ͕ՄೳͱͳΔ.. ͋Δ Compression graph ͷ PageRank ஋Λࢉग़͠,Cluster ͱ Hub ʹର͢ΔϥϯΩϯάΛ‫ٻ‬ΊΔ. ͜ͷ࣌, ҟͳΔ 2 ͭ. 5. ߟ࡯. ͷ Cluster ʹଐ͢ΔϊʔυؒͷΤοδͷΈΛߟྀ͠,Cluster. ఏҊํ๏ʹରͯ͠ 4 ͭͷߟ࡯͢΂͖఺͕͋Δ.. ಺ͷϊʔυؒͷΤοδ͸ແࢹ͢Δ. ·ͨ, ಉ͡ Cluster ؒͷ. 1 ͭ໨ʹຊఏҊํ๏ͷଥ౰ੑΛߟ͑Δ. ฒྻ෼ࢄॲཧΛ. Τοδ͕ 2 ͭҎ্ଘࡏͯ͠΋ 1 ͭͷΈͷΤοδͱͯ͠ѻ. ߦ͍͍ͨ৔߹, ߟྀ͠ͳ͚Ε͹ͳΒͳ͍໰୊ͱͯ͠, ෼ׂ. ⓒ 2014 Information Processing Society of Japan. 4.

(5) Vol.2014-DBS-160 No.20 Vol.2014-OS-131 No.20 Vol.2014-EMB-35 No.20 2014/11/18. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ਤ 6. ղੳͷྲྀΕ. ͨ͠ॲཧͲ͏͠ʹؔ܎ੑ͕ແ͍͔Ͳ͏͔ߟ͑Δඞཁ͕͋. Δ. ͜ͷ෼ผํ๏ʹΑΓ, ΠϯͷΈͷΤοδΛॴ༗͍ͯ͠Δ. Δ. ຊఏҊํ๏͸ Cluster ಺ͷϊʔυΛ PageRank ʹͯղ. ϊʔυΛ੾Γམͱ͢͜ͱͰ PageRank ͷղੳ͕࣌ؒߋʹ୹. ੳ͢Δࡍʹฒྻ෼ࢄॲཧΛߦ͏͕,Cluster ಺ͷϊʔυ͸ଞ. ॖग़དྷΔͱߟ͑Δ.. ͷ Cluster ΍ Hub,Outlier ͱ͸Τοδʹͯ઀ଓ͞Ε͍ͯͳ. 4 ͭ໨ʹ΢ΣϒάϥϑͷΫϥελϦϯάʹֻ͔Δ࣌ؒʹ. ͍. ͢ͳΘͪ,Cluster ಺ͷϊʔυ͸ Cluster ಺ͷϊʔυؒ. ؔ͢Δ‫ݕ‬౼Ͱ͋Δ. ఏҊํ๏͸,PageRank ʹΑΔ΢Σϒά. ͷΈʹͯΤοδ͕͋Γ, ؔ܎ੑ͕͋Δ. Αͬͯ,Cluster ಺ͷ. ϥϑͷղੳʹલॲཧͱͳΔ΢ΣϒάϥϑͷΫϥελϦϯά. PageRank ղੳ͸ಠཱͨ͠ॲཧͱͳΓฒྻ෼ࢄԽ͕Մೳͱ. ࡞‫͕͋ۀ‬ΔͨΊ, ୯७ʹ PageRank ʹΑΔղੳΑΓ΋ॲཧ. ͳΔ.. ਺͕ଟ͘ͳ͍ͬͯΔ. ͦͷͨΊ, ΫϥελϦϯάॲཧ͸୹. 2 ͭ໨ʹղੳର৅ͱͳΓ͏Δ΢ΣϒάϥϑΛߟ͑Δ.SCAN. ࣌ؒͰऴΘΔ͜ͱ͕๬·͍͠. ࣮૷͢Δࡍ,SCAN ͷॲཧΛ. ͸૬‫܎ؔͳີʹޓ‬ੑ, ͢ͳΘͪ૬‫ͳີʹޓ‬Τοδ͕͋Δ෦. MapReduce ʹରԠͤͨ͞ PSCAN[14] ΍, Ϋϥελ܎਺͕. ෼Λ Cluster ͱͯ͠ൈ͖ग़͢. Αͬͯ, ղੳର৅ͱ͢Δ΢Σ. େ͖͍‫࣮ݱ‬ͷάϥϑߏ଄ʹରͯ͠ΫϥελϦϯάॲཧ࣌ؒ. ϒάϥϑʹ͸શମʹૈີ͕ଘࡏ͢ΔάϥϑͰ͋Δඞཁੑ. Λ୹ॖͰ͖Δվྑ‫ ܕ‬SCAN[15] ͕͋Γ, ͜ΕΒΛ༻͍Δ͜. ͕͋Δͱߟ͑Δ. ۩ମతͳղੳର৅ͱͳΔ΢Σϒάϥϑ͸,. ͱͰΑΓॲཧ࣌ؒΛ୹ॖ͢Δ͜ͱ͕ՄೳʹͳΔͷͰ͸ͳ͍. ΢ΣϒΛීวతʹΫϩʔϦϯάͨ͠άϥϑͰ͋Δ͜ͱ͕๬. ͔ͱࢥΘΕΔ.. ·͍͠. ຊఏҊํ๏Ͱ PageRank ղੳͷߴ଎Խ͕๬Ίͳ͍ ΢Σϒάϥϑ͸, ୯ҰυϝΠϯΛର৅ͱͨ͠άϥϑ΍ϒϩ άαΠτΛΫϩʔϦϯάͨ͠άϥϑ͸ղੳ͕࣌ؒ୹ॖͮ͠ Β͍ͱࢥΘΕΔ.. 6. MapReduce ʹΑΔఏҊํ๏ͷฒྻ෼ࢄԽ ຊఏҊํ๏͸ϊʔυ਺͕ԯ୯ҐҎ্ͷ΢Σϒάϥϑ͕ ղੳର৅ͱͳΔͨΊ, ΫϥελϦϯάॲཧͱ PageRank ʹ. 3 ͭ໨ʹΤοδͷѻ͍ʹؔ͢Δ‫ݕ‬౼Ͱ͋Δ. ‫ࡏݱ‬͸ SCAN. ΑΔղੳ͸ MapReduce Λ༻͍ͨฒྻ෼ࢄॲཧΛߦ͏ํ. ͷํ๏Λ࢖༻͠,Cluster ͱͷΤοδʹ஫໨ͯ͠ Hub ͱ Out-. ਑ΛऔΔ.MapReduce ͸େ‫ن‬໛σʔλΛฒྻ෼ࢄॲཧ͢. lier ͷ෼ผΛߦ͓ͬͯΓ, Τοδ͕͋Δ͔ͳ͍͔ͷΈΛ෼. ΔͨΊͷϑϨʔϜϫʔΫͰ͋Δ.Map ॲཧͰσʔλΛఆ. ผ৚݅ͱ͍ͯ͠Δ. ͜͜ʹΤοδͷຊ਺, ͢ͳΘͪΤοδʹ. ٛͨ͠ํ๏Ͱ෼ׂΛߦ͍,Reduce ॲཧͰఆٛͨ͠ํ๏Ͱ. ॏΈͷ৘ใΛ௥Ճ͢Δ. ͜ͷ৘ใͷ௥ՃʹΑΓ, ॏΈͷԼ‫ݶ‬. ෼ׂͨ͠σʔλΛऩू͠, ॲཧΛߦ͏.SCAN ʹؔͯ͠͸. ஋ͷᮢ஋Λઃఆ͠, ᮢ஋ʹຬͨͳ͍ॏΈ෇͖ΤοδΛॴ༗. PSCAN[14] Ͱ,PageRank ʹؔͯ͠͸ Data-intensive text. ͍ͯ͠ΔϊʔυΛ੾Γམͱ͢͜ͱͰ PageRank ͷղੳ͕ߋ. processing with MapReduce[16] Ͱ‫ ʹط‬MapReduce Ͱఆٛ. ʹߴ଎Խग़དྷΔͱߟ͑Δ. ͜ͷଞʹΤοδͷํ޲ʹΑΔ෼. ͞Ε͍ͯΔͨΊ,Web graph ͷ࠶ߏஙͰ͋Δ Cluster graph. ผख๏ʹ‫ݕ‬౼ͷ༨஍͕͋Δͱߟ͑Δ. ର৅ͱ͢Δϊʔυ͕. ͱ Compression graph ʹؔͯ͠ MapReduce ͷఆٛΛड़. ྆ํ޲ͷΤοδ, ͢ͳΘͪΠϯͱΞ΢τ྆ํͷΤοδΛॴ. ΂Δ.. ༗͍ͯ͠Δϊʔυͱ, ยํ޲ͷΈΤοδ, ͢ͳΘͪΠϯ·. ·ͣ,Cluster graph ʹ͓͚Δ MapReduce ʹ͍ͭͯड़΂. ͨ͸Ξ΢τยํͷΤοδΛॴ༗͍ͯ͠Δϊʔυͱʹ෼ผ͢. Δ.Key/Value ͸ද 1 ʹࣔ͢΋ͷΛ༻͍Δ. දதͷ label. ⓒ 2014 Information Processing Society of Japan. 5.

(6) Vol.2014-DBS-160 No.20 Vol.2014-OS-131 No.20 Vol.2014-EMB-35 No.20 2014/11/18. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ͸ϊʔυʹ෇͍͍ͯΔ Cluster ΍ Hub,Outlier ͜ͱͰ͋. Hub ʹΑΔϥϯΩϯάΛ࡞੒͢Δ. ͦͷ‫ޙ‬,Cluster graph. Γ,node ͸ϊʔυʹ‫ݻ‬༗Ͱ༩͑ΒΕ͍ͯΔ ID,outdegree. ͷ PageRank ஋Λࢉग़͠,Cluster ಺ͷϊʔυʹΑΔϥϯΩ. ͸ϊʔυ͔Βग़͍ͯΔϦϯΫઌͷ node ͷ͜ͱΛࣔ͢. ·. ϯάΛ࡞੒, Ϛʔδ͢Δ.Cluster ಺ͷϊʔυʹର͢Δϥϯ. ͨ,Cluster ͱ Hub ʹ͸ͦΕͧΕ‫ݻ‬༗ͷ ID ͕༩͑ΒΕ͍ͯ. ΩϯάΛ‫ٻ‬ΊΔ࣌,Cluster ֎ͷϊʔυؒͷΤοδ͸ແࢹ͢. Δ΋ͷͱ͢Δ.. ΔͨΊ, ͓‫͍ޓ‬ͷ Cluster ͸ؔ܎ੑ͕ແ͘ͳΓ, ฒྻ෼ࢄॲ. ද 1. Cluster graph ʹ͓͚Δ Key/Value. Reduce. ͨΓͷ PageRank ͷղੳର৅ͱͳΔϊʔυͱΤοδ͕‫ݮ‬গ. Key. Value. label. node. ͢Δ. Ҏ্ΑΓ,PageRank ͷղੳ࣌ؒΛ୹ॖ͢Δ͜ͱ͕ग़. output. label. node, outdegree. དྷΔ. ͜ΕʹΑΓ,PageRank Λ༻͍͍ͯΔ‫ࡧݕ‬Τϯδϯͳ. input. Cluster ID. node, outdegree. ͲͰ, ΑΓߴ౓ͳ‫݁ࡧݕ‬ՌΛฦ͢͜ͱ͕ՄೳʹͳΓ, ৘ใࣾ. output. node. outdegree. ձʹ͓͚Δ඼࣭ͷߴ͍αʔϏεΛఏ‫͢ڙ‬Δ͜ͱʹߩ‫͖Ͱݙ‬. input Map. ཧ͕ՄೳͱͳΔ. ߋʹ, ΫϥελͰ੾Γ෼͚Δ͜ͱͰ 1 ճ͋. Δ. ࠓ‫ޙ‬͸࣮‫ݧ‬Λߦ͍, ຊఏҊํ๏͕Մೳ͔‫ূݕ‬Λߦ͏༧ఆ. Cluster graph ʹ͓͚Δ MapReduce ͸, ·ͣ Map ॲཧͱ. Ͱ͋Δ. ՄೳͰ͋Ε͹, ‫ࡏݱ‬͸ SCAN Λར༻͍ͯ͠Δ͕, ଞ. ͯ͠,input Ͱ͸,Cluster ΍ Hub,Outlier ͷϥϕϧΛ Key ͱ. ͷΫϥελϦϯάํ๏Ͱ΋ఏҊํ๏͕࣮‫͖Ͱݱ‬ΔՄೳੑ͕. ͠, ͦΕͧΕʹରԠ͢Δ node Λ Value ʹૠೖ͢Δ.output. ͋ΔͱࢥΘΕΔͨΊ, ௥ՃͰ࣮‫ݧ‬Λߦ͏༧ఆͰ͋Δ.. Ͱ͸,Value ͷ node ʹରԠ͢Δ outdegree Λ௥Ճ͢Δ. ࣍ʹ. Reduce ॲཧͱͯ͠,input Ͱ͸,Key ͔Β Cluster ͷϥϕϧ. ࢀߟจ‫ݙ‬. ͕෇͍ͨ΋ͷΛऩू͢Δ.output Ͱ͸,Value ʹ֨ೲ͞Εͯ. [1]. ͍Δ node Λ Key ʹૠೖ͢Δ.Reduce ॲཧΛ Cluster ID ͝ ͱʹ‫܁‬Γฦ͠, શͯͷ Cluster graph Λ࡞੒͢Δ.. [2]. ࣍ʹ,Compression graph ʹ͓͚Δ MapReduce ʹ͍ͭͯ ड़΂Δ.Key/Value ͸ද 2 ʹࣔ͢΋ͷΛ༻͍Δ. ද 2. [3]. Compression graph ʹ͓͚Δ Key/Value Key. Value. input. label. node. Map. output. label. node, outdegree. input. Hub ID. node, outdegree. Reduce. output. Hub ID. Cluster ID. Map ॲཧʹؔͯ͠͸ Cluster graph ͱಉ͡ॲཧΛߦ͏.Re-. [4]. [5] [6]. duce ॲཧͱͯ͠,input Ͱ͸,Key ͔Β Hub ͷϥϕϧ͕෇͍ ͨ΋ͷΛऩू͢Δ. ऩू‫ޙ‬,Value ͷ outdegree ͔Β, Ͳͷ. Cluster ͱ઀ଓ͍ͯ͠Δͷ͔Λௐ΂,Cluster ID Λ output ͷ Value ʹ௥Ճ͢Δ.Reduce ॲཧΛ Hub ID ͝ͱʹ‫܁‬Γฦ. [7]. ͠,Compression graph Λ࡞੒͢Δ.. 7. ͓ΘΓʹ ຊ‫Ͱڀݚ‬͸, ΢ΣϒάϥϑΛ PageRank ͷղੳ͕ฒྻ෼ ࢄॲཧՄೳͳάϥϑ΁࠶ߏஙΛߦ͍,PageRank ͷղੳΛߦ. [8]. [9]. ͏ࡍʹฒྻ෼ࢄॲཧΛ༻͍Δ͜ͱͰ, ղੳʹඞཁͳ࣌ؒΛ୹ ॖ͢Δํ๏ΛఏҊ͢Δ. ఏҊํ๏ʹΑΔ΢Σϒάϥϑղੳ. [10]. ํ๏͸,3 ͭͷεςοϓͰߦΘΕΔ.1 ͭ໨͸,SCAN Λ༻͍ ͯ Web graph ΛΫϥελϦϯά͠ Cluster ͱ Hub,Outlier. [11]. ʹϊʔυ෼ผ͢Δ.2 ͭ໨ʹ,PageRank ͷղੳ͕ฒྻ෼ࢄॲ ཧՄೳʹ͢ΔͨΊ,Cluster ͱ Hub Λ༻͍ͨ Compression. graph ͱ Cluster ಺ͷ΢ΣϒάϥϑͰ͋Δ Cluster graph ͷ 2 छྨͷάϥϑΛ࡞੒,Web graph Λ࠶ߏங͢Δ.3 ͭ໨ ͸,Compression graph ͷ PageRank ஋Λࢉग़͠,Cluster ͱ. ⓒ 2014 Information Processing Society of Japan. [12]. Brin, S. and Page, L.: The anatomy of a large-scale hypertextual Web search engine, Computer networks and ISDN systems, Vol. 30, No. 1, pp. 107–117 (1998). Kleinberg, J. M.: Authoritative sources in a hyperlinked environment, Journal of the ACM (JACM), Vol. 46, No. 5, pp. 604–632 (1999). Kumar, R., Raghavan, P., Rajagopalan, S. and Tomkins, A.: Trawling the Web for emerging cyber-communities, Computer networks, Vol. 31, No. 11, pp. 1481–1493 (1999). Reddy, P. K. and Kitsuregawa, M.: An approach to relate the web communities through bipartite graphs, Web Information Systems Engineering, 2001. Proceedings of the Second International Conference on, Vol. 1, IEEE, pp. 301–310 (2001). Netcraft: October 2014 Web Server Survey. Buehrer, G. and Chellapilla, K.: A scalable pattern mining approach to web graph compression with communities, Proceedings of the 2008 International Conference on Web Search and Data Mining, ACM, pp. 95–106 (2008). ย੉߂থɼ্ాߴಙɼࢁ໊ૣਓɿLittleWeb: ྨࣅϊʔυू ໿ʹΑΔ Web άϥϑѹॖख๏ɼThe 2nd Forum on Data Engineering and Information Management, DBSJ, pp. E1–4 (2010). Kohlsch¨ utter, C., Chirita, P.-A. and Nejdl, W.: Efficient parallel computation of pagerank, Advances in information retrieval, Springer, pp. 241–252 (2006). Wicks, J. and Greenwald, A.: Parallelizing the computation of pagerank, Algorithms and Models for the WebGraph, Springer, pp. 202–208 (2007). Kamvar, S., Haveliwala, T., Manning, C. and Golub, G.: Exploiting the block structure of the web for computing pagerank, Stanford University Technical Report (2003). Xu, X., Yuruk, N., Feng, Z. and Schweiger, T. A.: Scan: a structural clustering algorithm for networks, Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, ACM, pp. 824–833 (2007). Boldi, P. and Vigna, S.: The webgraph framework I: compression techniques, Proceedings of the 13th international conference on World Wide Web, ACM, pp.. 6.

(7) ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. [13]. [14]. [15]. [16]. Vol.2014-DBS-160 No.20 Vol.2014-OS-131 No.20 Vol.2014-EMB-35 No.20 2014/11/18. 595–602 (2004). γϡ΢ςΠɼɹยࢁ‫܆‬ɿࢉज़ූ߸Λ༻͍ͨ΢Σϒάϥϑ ද‫ݱ‬ͷͨΊͷѹॖํ๏ɼThe 6nd Forum on Data Engineering and Information Management, DBSJ, pp. D6–1 (2014). Zhao, W., Martha, V. and Xu, X.: PSCAN: A Parallel Structural Clustering Algorithm for Big Networks in MapReduce, Advanced Information Networking and Applications (AINA), 2013 IEEE 27th International Conference on, IEEE, pp. 862–869 (2013). Ԙ઒ߒতɼ౻‫ݪ‬༃޺ɼَ௩ɹਅɿߏ଄తྨࣅ౓ʹ‫ͮ͘ج‬ά ϥϑΫϥελϦϯάͷߴ଎ԽɼThe 6th Forum on Data Engineering and Information Management, DBSJ, pp. D6–2 (2014). Lin, J. and Dyer, C.: Data-intensive text processing with MapReduce, Synthesis Lectures on Human Language Technologies, Vol. 3, No. 1, pp. 1–177 (2010).. ⓒ 2014 Information Processing Society of Japan. 7.

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